Volume growth of horospheres in diagonalizable Heintze groups
Differential Geometry
2025-05-23 v1
Abstract
We study the volume growth of horospheres in a Heintze group of the form R ___ A R d with A a diagonal derivation. We conclude that the isometry and quasi-isometry classes of horospheres (with their intrinsic geometry) coincide. Furthermore, if A is not a scalar multiple of the identity, then there are exactly two such classes, characterized by their volume growth, which we calculate explicitly.
Cite
@article{arxiv.2505.16450,
title = {Volume growth of horospheres in diagonalizable Heintze groups},
author = {Gilles Courtois and Pablo Lessa and Emiliano Sequeira},
journal= {arXiv preprint arXiv:2505.16450},
year = {2025}
}